Abstract
We investigate monogamy relations related to the Renyi- $$\alpha $$ entanglement and polygamy relations related to the Renyi- $$\alpha $$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $$\mu $$ th power of Renyi- $$\alpha $$ entanglement with $$\alpha \in [(\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$$ for $$\mu \ge 2$$ , and polygamy relations satisfied by the $$\mu $$ th power of Renyi- $$\alpha $$ entanglement of assistance with $$\alpha \in [(\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$$ for $$0\le \mu \le 1$$ . These relations are shown to be tighter than the existing ones.
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